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Using a sharp knife, cut the salmon into slices about ½cm thick (if there's skin on your salmon, leave it behind as you cut each slice). Tear the smoked salmon into pieces.
Cut the potatoes into wafer thin slices as if you were making Dauphinoise potatoes. It’s best (and certainly quickest) to do this with a mandoline.
Heat oven to 180C/160C fan/gas 4 and put in a baking sheet to heat up. Mix the creams and the milk in a large saucepan, and bring to just under the boil. Add the potatoes and cook gently for 5 mins, carefully turning the potatoes over from time to time. Cut the beets into slices about 2mm thick.
Season the potatoes and cream and butter a 22 x 30cm baking dish. Spoon half of the potatoes into the dish and spread them out. Put half the beetroot on top of that, then half the fish. Season and add half the dill. Now add the rest of the beetroot and fish, seasoning again and adding the dill. Spoon the rest of the potatoes on top. You don’t need to arrange the top layer of potatoes nicely unless you really want to.
Bake for 1 hr, or until the potatoes are completely tender and the top is bubbling (it may need an additional 10 mins). Serve with a green salad or, if you want something more comforting, warm cabbage.